Big Idea:
Students will work with a partner to discover two more theorems as they explore why ASA and AAS congruence proves triangles are congruent.

This do now asks students to identify that two triangles are congruent using SAS. Depending on time limits in your class, this could be utilized as a formative assessment of SAS. This Do Now is a great chance to review a key term, included angle, which mirrors a key vocabulary word for this lesson, included angle.

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You can give students time in class today to work on their proof, and may want to require that the next class, students have a rough draft of their proof ready to hand in. If you also want students to test-shoot a video, this would be the time. The documents for this project can be found here.

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After reviewing the explorations with students, we can now introduce the formal definitions of ASA and AAS. One extension for this lesson is removing the formal definitions and asking students to write their own based on the explorations (MP3 and MP8).

Following up a quick brainstorming session on the methods that we have learned to show triangles are congruent, students can work on the 3 practice proofs to identify how (if possible!) we can determine that these triangles are congruent. You may want to reinforce that AAA is NOT a congruence theorem since this may or may not have come up in class yet. There is also a practice proof which teachers can walk students through using either a flow proof or 2-column proof.

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Resources

After completing the practice proof as a whole class, students can work on two proofs for extra in-class practice or for homework. You can ask students to complete the proofs as either 2-column proofs or flow proofs. We can extend this homework by asking students to do both!

The exit ticket asks students to identify that ASA is the congruence theorem needed to prove two triangles are congruent. If time remains in class, students can come to the board and explain their reasoning (MP3).